As a matter of fact, they tell you NOT to bring any luggage with you when going through customs between cruises. They want the line to move a quickly & smoothly as possible without people dragging things with them.

This will be my first time doing a back to back cruise, do I have to disemdark with all my bags & then come aboard again ?

I've also done back to back to back cruises on the same ship.
Only went thru C&i once . That was in Vancouver on our way to a
NB then SB cruise to Alaska from LA.
B2B cruises only have C&I when you board in Vancouver.
In 2008 on a B2B on RCI in Port Canaveral we didn't even have to leave
the ship.